2021 Fiscal Year Annual Research Report
Index theorems in scattering theory: beyond a finite number of bound states
| Project/Area Number |
18K03328
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| Research Institution | Nagoya University |
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Principal Investigator |
Richard Serge 名古屋大学, 多元数理科学研究科(国際), G30特任教授 (70725241)
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Keywords | Scattering theory / Wave operators / Decay estimates / Reproduction number / Epidemic propagation |
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| Outline of Annual Research Achievements |
The research activities have been adapted to the COVID-19 context, and have been centered on the following 3 topics:
1) With N. Tsuzu, we investigated the spectral and scattering theory of operators acting on topological crystals perturbed by infinitely many new edges. The setting of topological crystals corresponds to the most general framework for studying discrete periodic structures and their perturbations. The results have already been published.
2) With R. Tiedra de Aldecoa we have introduced a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. The framework is general enough for accommodating evolution groups generated by self-adjoin operators or dynamical systems generated by iteration of a fixed unitary operator. The result of these investigations have been submitted for publication.
3) With T. Miyoshi, Q. Sun, C. Sun, and N. Tsuzu, we have completed the investigations on a new approach for computing the effective reproduction number based on data assimilation. This reproduction number plays a key role in the propagation of epidemics, and our results have directly been applied to the current COVID-19 epidemic. Two papers have been submitted for publication, and one has already been accepted.
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